Cell motility goes in steps - protrusion, graded adhesion, contraction and forward translocation of the cell body. In general, protrusion is based on growth of actin arrays, adhesion depends on rapid dynamics of adhesion proteins, and myosin tendency to contract actin gel leads to the forward translocation. Cells move through diverse environments by employing many types of motile appendages and locomotory behaviors. We concentrate on the well studied motile appendage called lamellipodium - thin branched actin-myosin network deployed by many cells on flat surfaces. In the lamellipodium, molecular processes self-organize into a complex molecular machine executing a coherent mechanical action. As a result of decades of intense study, molecular inventory and general principles of steady lamellipodial locomotion are becoming clear. However, crucial physiological processes of wound healing, metastasis and tissue development require elucidation of unsteady cell movements. Besides physiological and clinical applications, quantitative understanding of such movements is a fundamental problem of cell biology and a critical test of our fledgling knowledge of active self-organizing cytoskeleton. Specifically, there is little understanding of how cells initiate motility, turning and splitting. Though there is a significant role for biochemical pathways regulating these processes, we aim to understand their mechanics by studying fish epithelial keratocytes that have an advantage of smooth integration of the motility steps. Computational modeling is an indispensable tool of discovery, so we propose a modeling/experimental investigation of the unsteady movements. Preliminary data and modeling hint that interdependence of force-generating protein distributions and cell movement and geometry underlies cell polarization, turning and splitting. Specifically, we hypothesize that the mechanism of motility initiation is a positive feedback in which the weakening of adhesion at the prospective rear of an initially symmetric cell causes local increase of actin flow, which further increases adhesion breakage. This feedback leads to irreversible asymmetric flows and re-distribution of myosin, actin and adhesions that polarize the cell. Similarly, asymmetric release of adhesions at the cell rear coupled with graded actin turnover and skewed actin flow creates a positive feedback generating cell turning. Finally, we hypothesize that having excess membrane or insufficient actin causes increased inherent fluctuations of actin density in the cell amplified by myosin-generated instabilities leading to uneven protrusions and to cell splitting. We will test these hypotheses by developing models of the viscoelastic contractile actomyosin network in the moving-boundary lamellipodium. We will simulate continuous deterministic and stochastic discrete models and predict key proteins' distributions, flows and forces, as well as cell shapes and speeds. We will calibrate and test the models by comparing the predictions with data obtained from wild type and perturbed cells. This work will result in advanced understanding of cell motility, and will also produce broadly applicable novel mathematical tools as well as mathematical model components that can be integrated with existing models of cell migration.